Stress has six components: three normal stresses and three shear stresses.

Pressure is generally concerned with only the stress normal to the surface, which ignores the other five stresses.

If you have a fluid that carries zero shear stress, then it can only provide a normal stress to a solid body.

If you have  solid body in contact with another solid body and there is friction at the interface, then it is possible to transmit a normal contact stress and two shear stresses at the surface, but that ignores three other stresses.

It is only if you have continuous material that you can transmit all six components of stress across an imaginary plane.